Quantum Phase Transitions in Spin-Lattice Systems

We present a theory of the anisotropy-tuned quantum phase transition between spin-nematic and spin-Peierls phases in $S=1$ systems with significant biquadratic exchange interactions. Based on quantum Monte Carlo studies on finite-size systems, it has been proposed that this phase transition is second order with new deconfined fractional excitations that are absent in either of the two phases. The possibility of a weak first-order transition, however, cannot be ruled out. To elucidate the nature of the transition, we construct a large- $N$ $\text{SO}(3N)$ model for this phase transition and find in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit that the transition is generically of first-order. Furthermore, we find a critical point in the one-dimensional (1D) limit, where two transition lines, separating spin-nematic, ferromagnetic, and spin-Peierls phases, meet. Our study indicates that the spin-nematic phase is absent in 1D, while its correlation length diverges at the critical point. Predictions for $^{23}\text{N}\text{a}$ atoms trapped in an optical lattice, where the nematic to spin-Peierls quantum phase transition naturally arises are discussed.We present a theory of the anisotropy-tuned quantum phase transition between spin-nematic and spin-Peierls phases in $S=1$ systems with significant biquadratic exchange interactions. Based on quantum Monte Carlo studies on finite-size systems, it has been proposed that this phase transition is second order with new deconfined fractional excitations that are absent in either of the two phases. The possibility of a weak first-order transition, however, cannot be ruled out. To elucidate the nature of the transition, we construct a large-$N$ $\text{SO}(3N)$ model for this phase transition and find in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit that the transition is generically of first-order. Furthermore, we find a critical point in the one-dimensional (1D) limit, where two transition lines, separating spin-nematic, ferromagnetic, and spin-Peierls phases, meet. Our study indicates that the spin-nematic phase is absent in 1D, while its correlation length diverges at the critical point. Predictions for $^{23}\text{N}\text{a}$ atoms trapped in an optical lattice, where the nematic to spin-Peierls quantum phase transition naturally arises are discussed.

arXiv:0806.4192Physical Review BOct 24, 20087 citations

Quantum Phase Transitions in Random Spin Systems

Muyu Guo

Jan 1, 19950 citations

Quantum phase transitions beyond the Landau paradigm in a Sp(4) spin system

Yang Qi, Cenke Xu

We propose quantum phase transitions beyond the Landau's paradigm of Sp(4) spin Heisenberg models on the triangular and square lattices motivated by the exact $\text{Sp}(4)\ensuremath{\simeq}\text{SO}(5)$ symmetry of spin-3/2 fermionic cold atomic system with only $s$ -wave scattering. On the triangular lattice, we study a phase transition between the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ spin ordered phase and a ${Z}_{2}$ spin liquid phase; this phase transition is described by an O(8) sigma model in terms of fractionalized spinon fields, with significant anomalous scaling dimensions of spin order parameters. On the square lattice, we propose a deconfined critical point between the Neel order and the valence bond solid (VBS) order, which is described by the CP(3) model, and the monopole effect of the compact U(1) gauge field is expected to be suppressed at the critical point.We propose quantum phase transitions beyond the Landau's paradigm of Sp(4) spin Heisenberg models on the triangular and square lattices motivated by the exact $\text{Sp}(4)\ensuremath{\simeq}\text{SO}(5)$ symmetry of spin-3/2 fermionic cold atomic system with only $s$-wave scattering. On the triangular lattice, we study a phase transition between the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ spin ordered phase and a ${Z}_{2}$ spin liquid phase; this phase transition is described by an O(8) sigma model in terms of fractionalized spinon fields, with significant anomalous scaling dimensions of spin order parameters. On the square lattice, we propose a deconfined critical point between the Neel order and the valence bond solid (VBS) order, which is described by the CP(3) model, and the monopole effect of the compact U(1) gauge field is expected to be suppressed at the critical point.

arXiv:0803.3822Physical Review BJul 7, 200813 citations

Interplay of localisation and competing interaction channels: cascade of quantum phase transitions

A. M. Belemuk, N. M. Chtchelkatchev, Andrey V. Mikheyenkov +1 more

We investigate the interplay of localization, interactions and (pseudo)spin degrees of freedom on quantum states of particles on the lattice. Our results show that breaking the paradigm density-density interaction $U_0\gg$ (pseudo)spin-(pseudo)spin interaction $U_s$ will drive the sequence of quantum phase transitions (QPT), where (pseudo)spin state and particle ordering, in case of several particle species, on the lattice are strongly changed. QPT driven by competing interactions, $|U_s|\sim U_0$ , manifest itself in singularities of effective exchange integrals. $|U_s|\sim U_0$ implies a frustration when the interactions standing alone drive the system to different phases. Even at $U_s=0$ , there is typically a QPT induced by $U_s$ sign change. Vector cold atoms, Fermions or Bosons, on optical lattices are the state-of-the-art realization of our system where $U_s$ is tunable \textit{in situ}.We investigate the interplay of localization, interactions and (pseudo)spin degrees of freedom on quantum states of particles on the lattice. Our results show that breaking the paradigm density-density interaction $U_0\gg$ (pseudo)spin-(pseudo)spin interaction $U_s$ will drive the sequence of quantum phase transitions (QPT), where (pseudo)spin state and particle ordering, in case of several particle species, on the lattice are strongly changed. QPT driven by competing interactions, $|U_s|\sim U_0$, manifest itself in singularities of effective exchange integrals. $|U_s|\sim U_0$ implies a frustration when the interactions standing alone drive the system to different phases. Even at $U_s=0$, there is typically a QPT induced by $U_s$ sign change. Vector cold atoms, Fermions or Bosons, on optical lattices are the state-of-the-art realization of our system where $U_s$ is tunable \textit{in situ}.

arXiv:1602.02563Feb 8, 20160 citations

Quantum phase transitions in random spin systems

T. Senthil

Jan 1, 19970 citations

We present a theory of the anisotropy-tuned quantum phase transition between spin-nematic and spin-Peierls phases in

S=1

systems with significant biquadratic exchange interactions. Based on quantum Monte Carlo studies on finite-size systems, it has been proposed that this phase transition is second order with new deconfined fractional excitations that are absent in either of the two phases. The possibility of a weak first-order transition, however, cannot be ruled out. To elucidate the nature of the transition, we construct a large-

N

\text{SO}(3N)

model for this phase transition and find in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit that the transition is generically of first-order. Furthermore, we find a critical point in the one-dimensional (1D) limit, where two transition lines, separating spin-nematic, ferromagnetic, and spin-Peierls phases, meet. Our study indicates that the spin-nematic phase is absent in 1D, while its correlation length diverges at the critical point. Predictions for

^{23}\text{N}\text{a}

atoms trapped in an optical lattice, where the nematic to spin-Peierls quantum phase transition naturally arises are discussed.

s

-wave scattering. On the triangular lattice, we study a phase transition between the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ spin ordered phase and a

{Z}_{2}

spin liquid phase; this phase transition is described by an O(8) sigma model in terms of fractionalized spinon fields, with significant anomalous scaling dimensions of spin order parameters. On the square lattice, we propose a deconfined critical point between the Neel order and the valence bond solid (VBS) order, which is described by the CP(3) model, and the monopole effect of the compact U(1) gauge field is expected to be suppressed at the critical point.

U_0\gg

(pseudo)spin-(pseudo)spin interaction

U_s

will drive the sequence of quantum phase transitions (QPT), where (pseudo)spin state and particle ordering, in case of several particle species, on the lattice are strongly changed. QPT driven by competing interactions,

|U_s|\sim U_0

, manifest itself in singularities of effective exchange integrals.

|U_s|\sim U_0

implies a frustration when the interactions standing alone drive the system to different phases. Even at

U_s=0

, there is typically a QPT induced by

U_s

sign change. Vector cold atoms, Fermions or Bosons, on optical lattices are the state-of-the-art realization of our system where

U_s

is tunable \textit{in situ}.